Two centuries ago, Thomas Young performed the classic demonstration of the wave nature of light. He placed a screen with two tiny slits in front of a single light source, effectively converting it into a two-centered source. On a second screen far away, he saw a pattern of light and dark diffraction fringes, a well-known hallmark of wave interference. Along with later studies using particles instead of light, the experiment played a crucial role in establishing the validity of wave–particle duality, a puzzling concept that has ultimately become central to the interpretation of complementarity in quantum mechnanics. In a new twist on this classic experiment, the double slit (with light waves) has been replaced by a diatomic molecule (with electron waves). At ALS Beamline 10.0.1, researchers have shown that diatomic molecules can serve as two-center emitters of electron waves and that traces of electron-wave interference can be directly observed in precise measurements of vibrationally resolved photoionization spectra.

Why Do Matter-Waves Matter?

Understanding the detailed mechanisms leading to electron-wave interferences has become increasingly important because many contemporary techniques that probe the structure of matter on the atomic scale are based on the wave nature of the free electron. Electron diffraction as well as transmission and scanning electron microscopy rely on the fact that long-range crystalline order acts as a diffraction grating for the incoming electron wave. For spectroscopies utilizing energetic radiation, an ionized atom is the source of electrons that scatter coherently within the surroundings. The information that can be extracted is extremely sensitive to local electronic geometric structure. Furthermore, as the time resolution of structural methods rapidly reaches the pico-, femto-, and even attosecond scales, the interplay between geometric and electronic variables must be taken into account to understand the dynamic nature of these interferences. For example, in the photoionization of a diatomic molecule, electron-wave interferences, which depend on the distance between the two atoms, can track the variations of the electronic structure as the ionized molecule vibrates. Just as the set of atomic positions is the starting point of any crystallographic refinement or modeling, accurate electronic-state calculations will become an inherent part of the emerging ultrafast techniques.

Depiction of electron waves interfering with each other as they propagate outward from a diatomic molecule. Rendered by Etienne Plésiat.

In the 1960s, Howard Cohen and Ugo Fano conjectured that it should be possible to conduct a microscopic version of the double-slit experiment by photoionizing homonuclear (single-element) diatomic molecules. The emitted electrons, which are initially shared between the two indistinguishable atoms, would be "coherent" when their deBroglie wavelengths are comparable to the molecule's equilibrium interatomic distance. Under these conditions, Cohen and Fano predicted that electron-wave interference should affect the molecule's photoionization cross sections (i.e., the probability of ionization) for photoionization energies of a few hundred eVs (the extreme ultraviolet regime). The manifestations of this matter-wave interference have been actively sought in beautiful but time-consuming experiments that require "fixing in space" the molecular targets via complex detection schemes. In addition to the practical difficulties, such an approach required the introduction of arbitrary calibration parameters or fitting functions, leading to equivocal interpretations.

The work reported here takes another, more direct approach based on an elaborate, first-principles framework developed within the international group led by F. Martín (Autonomous University of Madrid). The analysis includes consideration of the vibrational transitions associated with valence-shell photoionization of diatomic molecules. One striking prediction was that values of the photoionization cross-section would oscillate around a value predicted by the Franck–Condon principle, which governs the likelihood of transitions involving electronic and vibrational states ("vibronic" transitions). The approach was made experimentally possible by the advent of high-brightness, third-generation light sources as well as significant progress in electron detection techniques able to distinguish the various vibrational states available to diatomic molecules.

The unique characteristics of extreme beam stability, powerful photon flux, and high resolving power offered at ALS Beamline 10.0.1 allowed the research team to access the underlying structure of the valence photoelectron bands and to reliably extract vibrational cross-sections over a wide photon energy range (20 to 300 eV). The experiments were performed on hydrogen (H2)—the simplest of all diatomics, homonuclear nitrogen (N2), and even the heteronuclear carbon monoxide (CO). Clear oscillations around the Franck–Condon values have been observed and interpreted as the distinct mark of Young's interferences. They are satisfactorily reproduced by first-principles calculations that do not require the introduction of any external arbitrary parameters or fitting functions.

Ratios of the vibrationally resolved photoionization spectra to the v′ = 2 cross section as a function of photon energy for the H2 molecule. Circles with error bars: experimental results; the different colors indicate different runs. Full black curve: theoretical results. Dashed-dotted line: Franck–Condon value. Similar data were obtained for N2 and CO.

These results on benchmark molecules constitute an important step toward extending this particular combination of detection technique and advanced modeling into a widely applicable structural tool for electron interferometry and holography by capitalizing on coherent photoemission. These multicenter interferences in the continuum are a very sensitive probe of electronic and geometric degrees of freedom. As such, they can track in real time the various couplings at play during the photoionization processes triggered by accelerator- or lab-based light sources that are rapidly developing around the world.

Research conducted by: S.E. Canton (Lund University, Sweden), E. Plésiat (Autonomous University of Madrid, Spain), J.D. Bozek (SLAC National Accelerator Laboratory), B.S. Rude (ALS), P. Decleva (University of Trieste and the National Research Council, Institute of Materials, Italy), and F. Martín (Autonomous University of Madrid and the Madrid Institute for Advanced Studies in Nanoscience, Spain).

Research funding: Ministry of Science and Innovation (Spain) and COST (European Cooperation in Science and Technology). Operation of the ALS is supported by the U.S. Department of Energy, Office of Basic Energy Sciences.